28,969 research outputs found
Irregular and multi--channel sampling of operators
The classical sampling theorem for bandlimited functions has recently been
generalized to apply to so-called bandlimited operators, that is, to operators
with band-limited Kohn-Nirenberg symbols. Here, we discuss operator sampling
versions of two of the most central extensions to the classical sampling
theorem. In irregular operator sampling, the sampling set is not periodic with
uniform distance. In multi-channel operator sampling, we obtain complete
information on an operator by multiple operator sampling outputs
Role of Phonon Scattering in Graphene Nanoribbon Transistors: Non-Equilibrium Green's Function Method with Real Space Approach
Mode space approach has been used so far in NEGF to treat phonon scattering
for computational efficiency. Here we perform a more rigorous quantum transport
simulation in real space to consider interband scatterings as well. We show a
seamless transition from ballistic to dissipative transport in graphene
nanoribbon transistors by varying channel length. We find acoustic phonon (AP)
scattering to be the dominant scattering mechanism within the relevant range of
voltage bias. Optical phonon scattering is significant only when a large gate
voltage is applied. In a longer channel device, the contribution of AP
scattering to the dc current becomes more significant
A new approach to the 2-variable subnormal completion problem
We study the Subnormal Completion Problem (SCP) for 2-variable weighted
shifts. We use tools and techniques from the theory of truncated moment
problems to give a general strategy to solve SCP. We then show that when all
quadratic moments are known (equivalently, when the initial segment of weights
consists of five independent data points), the natural necessary conditions for
the existence of a subnormal completion are also sufficient. To calculate
explicitly the associated Berger measure, we compute the algebraic variety of
the associated truncated moment problem; it turns out that this algebraic
variety is precisely the support of the Berger measure of the subnormal
completion
Theoretical correction to the neutral meson asymmetry
Certain types of asymmetries in neutral meson physics have not been treated
properly, ignoring the difference of normalization factors with an assumption
of the equality of total decay width. Since the corrected asymmetries in
meson are different from known asymmetries by a shift in the first order of CP-
and CPT-violation parameters, experimental data should be analyzed with the
consideration of this effect as in meson physics.Comment: 7 page
Hyponormality and subnormality for powers of commuting pairs of subnormal operators
Let H_0 (resp. H_\infty denote the class of commuting pairs of subnormal
operators on Hilbert space (resp. subnormal pairs), and for an integer k>=1 let
H_k denote the class of k-hyponormal pairs in H_0. We study the hyponormality
and subnormality of powers of pairs in H_k. We first show that if (T_1,T_2) is
in H_1, then the pair (T_1^2,T_2) may fail to be in H_1. Conversely, we find a
pair (T_1,T_2) in H_0 such that (T_1^2,T_2) is in H_1 but (T_1,T_2) is not.
Next, we show that there exists a pair (T_1,T_2) in H_1 such that T_1^mT_2^n is
subnormal (all m,n >= 1), but (T_1,T_2) is not in H_\infty; this further
stretches the gap between the classes H_1 and H_\infty. Finally, we prove that
there exists a large class of 2-variable weighted shifts (T_1,T_2) (namely
those pairs in H_0 whose cores are of tensor form) for which the subnormality
of (T_1^2,T_2) and (T_1,T_2^2) does imply the subnormality of (T_1,T_2)
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